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Sedums are good for hot dry baked areas, and there are lots of Sedums, some low growing some a foot or 2 tall. Just about any succulent plant. Even Creeping phlox, which are out already at my local Home depot. At my last house, I had a whole hillside of them in pink, white and Lavender colors. And after the house was sold, the guy ripped it all out, and weedwacks the hillside. The stuff was filling in nicely, too. I guess he wanted to make it "his". But anyhow, look up full sun, drought resistant plants online too. Whatever you choose will need watering and mulching the first year. And keep weeds out also. That is the pain in the butt part. I would get rid of the grass you have there now. Whether you use round-up or smother the weeds with a tarp or weed block fabric. Of course don't use the round-up 365.

There are many reasons that the grass is dying.
Do you have grubs, bad outbreak of crab grass, poor soil, builders blend quality grass seed, fertilize proberly ( too much, too little, wrong kind) Some grass seed is "annual" variety and may die out at the end of the year.
Once you have any of the above identified and undercontrol, the grass will be easier to maintiain. ANd easier than digging and planting, weeding and mulching a bed of ground cover.
I agree that the low growing sedum would be a good choice. Hopefully you can find in sold in a large tray. But be prepared for the next few years to water, mulch and weed. The nice part about sedum is that it is walkable and can tolerate foot trafic.
I like your idea and this is lots you can do.
good luck
Mike

This post was edited by plantman56 on Tue, Apr 8, 14 at 8:04

You know, instead of beating your head against a wall, figuratively speaking, why don't you create a rock garden in that corner? Or plant knockout roses that require little care? For whatever reason, grass just doesn't want to grow there. How about doing a partial retaining wall just at the corner and planting some vines to spill over and cover the area? Grass is hard to maintain on a slope. We have the same issue in our yard. We have torrential rains down here in MS. It's almost impossible to keep grass in an area that turns into a river at the front of our yard. We have a very wide yard....about 2 acres. My long-term plan is to turn the front into a cottage garden which means eliminating the grass on the slope.

I am very SORRY to all of the people that were kind enough to share there thoughts on one of my landscape headache. Life just got in the way I know most folks have been in my shoes. I will follow up asap. Thanks and sorry again.